A Structural Model of the Unemployment Insurance Take-up

Sylvie Blasco∗

GAINS, University of Aarhus,CREST and IZA

Francois Fontaine†

BETA-CNRS,LMDG and IZA.

January 2012 - IN PROGRESS‡

Abstract

A large fraction of the eligible workers do not claim the unemployment insurance when they areunemployed. This paper provides a structural framework to identify clearly, through the esti-mates, the economic mechanisms behind take-up. It incorporates take-up in a job search modeland accounts for the determinants of claiming, especially the level of the unemployment benefitsand the practical difficulties to make a claim. It provides a simple way to model selection intoparticipation and sheds new light on the link between the job search and the claiming efforts.We estimate our model using a unique administrative dataset that matches a linked employer -employee data and the records of the national employment agency.

Keywords: Unemployment Insurance Take-up, Job SearchJEL Classification numbers: J64, J65, C41

∗Address : Universite du Maine, Av. Olivier Messiaen, 72085 Le Mans Cedex 9, France ; Email:sylvie.blasco@univ-lemans.fr†University of Nancy 2, Email: francois.fontaine@univ-nancy2.fr.‡We thank Jesper Bagger, Sebastian Buhai, Sam Kortum, David Margolis, Dale Mortensen, Fabien Postel-Vinay,

Jean-Marc Robin, Chris Taber and participants at the Tinbergen Institute internal seminar, CREST-INSEE, Nancyand Royal Holloway seminars, the ESEM conference, the AFSE, IZA-Labor Market Policy Evalation, LMDG, T2Mworkshops for comments and discussions. This is a preliminary version of the paper, the readers are invited to checkon the authors’ websites for newer versions.

1

1 Introduction

Unemployment insurance (UI hereafter) has been designed to insure workers against the loss of

income. However, like most welfare benefits (Currie [2006], Hernanz et al. [2004]), the take-

up among eligibles is far from 100%. The unemployment insurance take-up rate is estimated to

range between 40% and 70% in the US (Blank and Card [1991], Anderson and Meyer [1997], McCall

[1995]) and between 60% and 80% in Canada and the UK (Storer and Van Audenrode [1995], DWP

[2008]). Theoretical studies and empirical evaluations of the UI system usually ignore this problem

and assume that all eligible workers receive benefits (see Kroft [2008] for a notable exception).

However, the empirical low take-up rates question this assumption and a study of the efficiency

of the actual UI systems should take this empirical evidence seriously. For that purpose, it is

first crucial to investigate the determinants of the take-up. This paper provides and estimates a

structural model to adress this issue.

It builds on the existing welfare benefits take-up literature (see Moffit [1983] and Currie [2006]

for a recent survey). In our framework, take-up is the result of a utility-maximizing decision which

accounts for the gains of participating in the UI system (the expected unemployment compensation

or the job search assistance) and the expected costs which depend on the practical difficulties to

make a claim, which are modeled as frictions in the claiming process.

An important feature of our model is its ability to explicitly take into account the link between

the job search activity and the take-up behavior. This is crucial to estimate the impact of the

take-up rate on the cost of unemployment. Indeed, some eligibles are not observed as receiving un-

employment benefits because they leave unemployment very quickly. If a worker expects a relatively

low unemployment duration and faces claiming frictions, he has few incentives to participate in the

UI system. The existing literature does not account for this link explicitly. Moreover, it uses static

choice models (McCall [1995], Blank and Card [1991], Anderson and Meyer [1997]), while we argue

that one must take into account the duration of the insured and uninsured unemployment spells.

In terms of welfare cost, it is crucial to look at the duration of the non insured unemployment spell

along with the take-up rate per se. Especially, we show that some workers receive unemployment

benefits after a relatively long period of uninsured unemployment. For these workers, the existing

frictions in the claiming process are very costly.

We provide a dynamic framework in which we model both the worker’s job search and his effort

to collect information to file for UI benefits. We go beyond the idea of a binary choice between

claiming or not by introducing the idea of claiming effort. This allows us to account for temporary

non take-up, i.e. to study the distribution of durations without receiving benefits, and not to limit

the analysis to the share of the eligible population which receives the unemployment insurance.

Interestingly, our model exhibits selection in the participation in the UI system and substitution

2

between job search activities and the claim for the unemployment compensation.

Rather than estimating a reduced-form hazard rate model, we proceed to a structural estimation

using a unique administrative dataset that follows individuals, employees and unemployed workers,

(FH-DADS)1. Most of the existing studies are using survey data, but a notable exception is An-

derson and Meyer (1997). When concerned with the analysis of take-up behaviors, administrative

data presents two main advantages. They are usually more reliable and larger than ad hoc surveys.

Moreover, they include short unemployment spells (lower that a month) and make it possible to

sample from inflows rather than the stock. This is all the more important to our purpose, as

we are dealing with a dynamic set up where temporary non take-up is suspected. In comparison

with Anderson and Meyer, our estimations are directly based on a structural model of claiming

behaviors where job search behaviors are endogenous and where claiming may take time and effort.

The advantage of a structural model is its ability to identify clearly, through the estimates, the

economic mechanisms behind take-up. The decomposition of the participation process is crucial to

provide advices to improve the effectiveness of the UI system as an insurance device (Heckman and

Smith [2004]). Moreover, we are able to estimate the welfare costs of claiming frictions.

The model is presented along with stylized facts in section 2. In section 3, we discuss our

dataset, the empirical specification and the estimation strategy. Section 4 presents our results.

2 A job search model with endogenous unemployment insurance

take-up

The features of the French UI system and some stylized facts

We investigate the UI system ongoing in France between July 2001 and December 2002. The model

mimics the main features of this system, which is largely similar to the existing systems in most of

the OECD countries. The French system provides constant unemployment benefits for a limited

period of time. All workers registered at the unemployment agency are helped and followed during

their job search (see Crepon et al. [2005] for a description of the French active policy). Regular

interviews with caseworkers and, for some workers, participation in training programs create non

monetary costs/benefits of participation and are likely to affect job search behaviors (see Black et

al. [2003])2. Lastly, until a recent change, the sanction rate was almost null. For that reason and

for sake of simplicity, we do not model sanctions.

1FH, which stands for Fichier Historique are the records of the French national employment agency, while DADS,which means Declarations Annuelles des Donnees Sociales are the French administrative linked employer-employeedata.

2For example, the UI can cause a shift from informal job search methods (which cannot be observed by theemployment agency) to observable methods (van den Berg and van der Klaauw [2006]).

3

The receipt of the unemployment compensation is not automatic. Eligibility depends on the

past employment duration. Although this rule is fairly simple, it is generally unknown and the

claiming process is complicated and time consuming. An unemployed worker has first to contact

his local unemployment agency. He has to fill a form, describing precisely his situation and has

to provide different documents to prove his entitlement rights. Eventually, he has to show up at

his local agency within the first week following his claim. Hence, to make successfully a claim, a

worker has to be informed, understand and follow different administrative steps.

0

5

10

15

20

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43

TU=0 TU=1

Figure 1: Distribution of unemployment duration by take-up status (in weeks). TU = 1 the workerreceive the unemployment insurance during his unemployment spell. TU = 0: the worker will notreceive the UI.

The analysis sample will be presented later but it is useful to provide some empirical evidence

before going into the model presentation. This evidence motivates the way we model the take-up of

the UI and give a preview of the potential economic mechanisms. Our sample only includes eligible

male workers between 30 and 50 years of age. In this sample, the take-up rate is around 40%. By

looking at the distribution of unemployment duration by take-up status (Figure 2), we see that a

huge fraction of workers who do not claim unemployment benefits (labelled TU = 0 in the Figure

2) leave unemployment very quickly suggesting that workers with good employment prospects do

4

not make efforts to claim for the unemployment benefits. Nevertheless, among workers who receive

unemployment benefits during their unemployment spell (labelled TU = 1 in Figure 2) the mean

duration without receiving any compensation is about 3 months. This shows that claiming takes

time and is potentially costly.

Finally, a logistic regression shows the determinants of the UI take-up probability. We replicate

here the empirical estimation mage in a number of existing studies on the subject, ignoring both

the endogeneity of unemployment duration and the dynamic nature of the problem. Results are

displayed in Table 1. The probability of receiving the unemployment compensation is positively

correlated with the average monthly wage in the worker’s previous job3. Since the amount of

unemployment benefits is positively linked with the past wage, the incentives to claim increase with

the wage. There is no clear pattern by occupation but the probability to receive UI is positively

correlated with the expected UI duration. These elements suggest that the worker trades off the

value of UI with existing transaction costs. Our model is designed to capture this trade-off and the

stylized facts presented above.

Table 1: Probability of UI receipt among entitled workers

Estimates s.d.Intercept -4.128∗∗∗ (0,171)log(past wage) 0,410∗∗∗ (0,025)Potential compensation duration(ref.: 4-7 months)

15 months 0,023 (0,056)30 months 0,075∗ (0,044)

Occupation (ref.: plant workers)Employees 0,212∗∗∗ (0,043)Technicians and associate prof. 0,097∗∗∗ (0,037)Managers and prof. -0,119∗∗∗ (0,044)

Significance at 1% level: ∗∗∗ ; at 10% level: ∗; standard errors in parenthesis.

Source: FH-DADS, 29 834 eligible non employment spells starting between 07/2001 and 12/2002.

The model

We provide a partial equilibrium job search model with infinitely lived agents. As it will be the

case in our estimations, we only consider workers eligible to the unemployment insurance. Time

is continuous and the labor market is at the steady state. We distinguish in our model three

unemployment states, denoted by j, depending on whether the unemployed worker is in the claiming

process (state N), receives the unemployment insurance (state P ) or has exhausted his rights (state

3The wage is computed using the job spells in the year before the entry into unemployment

5

L). In each of these states j, the individual chooses a job search effort (ej , with j = {N,P,L})and a reservation wage (Rj). The cost of search efforts is noted cj(ej) (with j = {N,P,L}), with

c(.) > 0, c(0) = 0, c′(.) ≥ 0 and c′′(.) > 0. We allow for the search technology, sum up by the

job arrival rate λj , to be different in each state. For sake of simplicity, the wage offer distribution

F (.) is not state dependent and the job acceptance rate thus reads λjej(1− F (Rj)) when in state

j = {N,P,L}.We model the take-up decision as the result of an effort to deal with the claiming frictions that

is the complexity of the administrative process. The claiming process is costly and takes time,

the worker has to understand the administrative requirements, collect the documents needed and

fill a claim. In state N , the claiming effort, noted δ, is chosen optimally and affects the duration

without compensation. The cost of claiming efforts is cγ(δ) and the cost function satisfies the same

properties as the cost of search effort. Claiming frictions are modelled in a similar way as search

frictions. An eligible worker switches from state N to P , where he receives the UI, at a rate γδ. γ

is thus an index of the frictions in the claiming process, in the spirit of the job arrival rates. One

of the aim of this paper is to get estimates of these claiming frictions together with evaluation of

the welfare cost they induce.

In each state j, the individual instantaneous utility uj is supposed to depend on his past em-

ployment wage w and we assume uj = u(aj + bjw). a stands for leisure or domestic production

which can depend on the individual’s status. We include w for two reasons. First, the unem-

ployment benefits are calculated using past wages4. More generally this can be thought as a very

stylized way to account for precautionary savings, that we do not model directly, or any form of

dependence between past wages and unemployment value. Remark that even for workers who get

an unemployment compensation (that is in state P ), bP cannot be interpreted as the replacement

ratio, but more generally as a statistical link we want to estimate.

We now introduce the value functions. We denote ρ the discount rate. The value of unemploy-

ment in state N , where the worker claims for benefits and searches for a job, reads:

ρVN (w) = u(aN + bNw)− cN (eN )− cγ(δ) +

λNeN

∫RN

(J(x)− VN (w))dF (x) + γδMax{VP (w)− VN (w), 0}

with J(x) the value of a new job with a wage x. Job search and claiming activities are simultaneous.

The worker chooses eN and δ to maxmize his intertemporal utility. The first order conditions and

4In France the replacement rate ranges between 57 and 75% depending on the previous wages. Since the definitionsof wage is different from the total labor income, the actual replacement rates are often lower.

6

the indifference condition defining the reservation wage are:

c′N (eN ) = λN

∫RN

∂J(x)

∂xF (x)dx (1)

c′γ(δ) = γMax{VP (w)− VN (w), 0} (2)

RN s.t. J(RN ) = VN (w) (3)

In some cases, the worker has no incentive to claim the unemployment benefits and thus his op-

timal claiming effort equals zero. This is especially true if the unemployment benefits are small

with respect to the claiming costs or if the worker expects his search technology to deteriorate

dramatically in state P (λP << λN ).

In state P , the worker searches for a job with a new technology and receives benefits. We

assume that the insurance ends, at each period, with a probability µ. In the actual UI system,

the insurance duration is not stochastic. However, this assumption simplifies the model and can

be seen as an appropriate simplification for two reasons. First, the fact that the worker can gain

the right to benefits extension if he works a little during his unemployment period (a system called

’activite reduite’, reduced activity) introduced some form of uncertainty. Moreover, the model and

the empirical investigation are mainly focused on the transitions between state N and P and not on

the exit rate profiles when the worker is in state P . What is thus crucial is to get the expectation of

the value of unemployment in this state right but not necessary to fit perfectly the exact exit rate

profiles in this state. Even if we agree that this is an imperfect assumption, we think that the gain

in term of computational time is sufficiently significant to justify it. If the end of the unemployment

insurance is taken as deterministic, the search intensity and reservation wage become functions of

the time spend in state P . This is perfectly feasible. However the estimation of the model requires

to solve it for each guess on the structural parameters and for each combination of the state

variables (w, any other form of heterogeneity and the time spends in unemployment if it is a state

variable). The estimation of the deterministic model is very cumbersome in practice. The use of a

stochastic framework reduces the dimension of the problem. This allow us to introduce unobserved

heterogeneity (see in the next section). For each worker, µ will be chosen in the estimation such

that 1/µ (the expected benefits duration) matches the ‘true’ benefits duration at the entry in state

P .

The value of unemployment in states P reads

7

ρVP (w) = u(aP + bPw)− cP (eP )

+ λP eP

∫RP

(J(x)− VP (w))dF (x) + µ(VL(w)− VP (w))

The optimal search intensity and reservation wage satisfy:

c′P (eP ) = λP

∫RP

∂J(x)

∂xF (x)dx (4)

RP s.t. J(RP ) = VP (w) (5)

The higher the duration of the insurance (that is the lower µ), the higher the reservation wage

and thus the lower the search intensity. Besides, as usual, the level of the insurance reduces the

search effort. In the last state, L, the worker is still looking for a job but no longer receives the

unemployment compensation. The value of unemployment reads:

ρVL(w) = u(aL + bLw)− cL(eL) + λLeL

∫RL

J(x)− VL(w)dF (x)

Eventually, for the sake of clarity, the definition of the value of employment J(x) is postponed to

the empirical specification.

2.1 How claiming and job search react to a change in the UI system?

What are the effects of a change in the UI design, especially a change in the replacement rate or in

the insurance duration? In our framework, they are not standard since the effort devoted in claiming

the UI and searching for a job interact. Consider again equations (1), (2) and (3). Reservation

wage depends on the value of unemployment in state N which is affected by the claiming frictions,

the generosity of the unemployment insurance but also by the relative efficiency of job search in

state N and P (λN vs λP ).

First, under simple conditions5, a rise in bP increases the value of unemployment in both N

and P states and thus the reservation wage, RN . In this case, the exit rate from unemployment

decreases in state N . The worker postpones his job search to state P and increases his claiming

effort since the unemployment insurance is more profitable. A decrease in the claiming friction

(a rise in parameter γ) or an improvement in the efficiency of job search in state P have the

5We abstract from the eligibility effect (Mortensen, 1977). A rise in the value of insured unemployment increasesthe value of employment and, in some cases, may decrease the reservation wage.

8

same effects. From these simple example, it becomes obvious that the take-up and the job search

behaviors interact. Estimation of the take-up behaviors requires a model encompassing both. This

paper provides such a model.

3 Empirical Application and Estimation Method

We begin this section by presenting the data and the selected sample, then we discuss the estimation

methods.

3.1 The data

The FH-DADS data6 are similar to the data used by Anderson and Meyer (1997). This is a

match of the yearly declarations of social data (DADS), where employers of the private and semi-

public sectors report earnings, hours and job duration of individuals they have employed during

the year, together with data from the insurance system. The original datasets are 1/24 nationally

representative samples7. The merge of these datasets includes any individual who appears in one

or another of these records between January 1st, 1999 and December 31st, 2004. A worker can

thus be included even if he did not experience any unemployment spell or, on the contrary, did not

experience any employment spell. The data are longitudinal and give information on the private

and semi-public sector back to 1976, on registered unemployment history back to 1993 and on

insured unemployment back to 1999.

The administrative nature of these data make them attractive for a study of non take-up. They

provide information on a daily basis and allow us to work on outflows from employment. We thus

observe all unemployment spells, even those of short duration. In addition, work history can be

traced back to 1976, and individuals are followed even when they move geographically (within

France). For each job in the private or semi-public sectors, we observe the start and end dates,

earnings and number of hours worked (after 1993). These information are used to predict eligibility

and to calculate the reference wage which determines the amount of benefits. Moreover, we observe

all insured unemployment spells the individual had between 1999 and 2004. As a result, we are

able to determine eligibility at the time of job separation and the take-up decision and timing.

The main drawback of this dataset, which is common to most of the dataset which only cover

the private sector, is that missing days in the employer-employee data do not necessary mean that

the individual was unemployed. Four main reasons may explain why an individual does not appear

6These data are available since June 2009 and are managed by the research and statistics department of the frenchministry of social affairs (DARES).

7Workers born on October of an even-numbered year are sampled.

9

in the FH-DADS dataset for a given period: he may be unemployed but not taking up UI, out

of the labour force, employed but not by an entity that is subject to the mandatory report, or

misidentified8. As a result, an individual who is observed neither in the DADS, nor in the records

of the national employment agency is not necessarily an unemployed worker who does not take up

unemployment insurance. Whether the individual is unemployed or inactive is however not relevant

to our purpose as long as we restrict our analysis to the entitled workers: if the individual exits the

labour force although he is entitled to compensation, he still forgoes money. Moreover, maternity

and sickness leaves do not generate an exit from employment in the DADS dataset, so the inactivity

periods we might worry about are essentially due to schooling, early and regular retirement and

entry into programmes of the social security system other than unemployment. We circumvent

these problem by considering in our analysis sample only male workers between 30 and 50 years of

age.

The fact that some jobs (public jobs and self-employment) are not reported in the DADS

sample is, on the contrary, more problematic. However, using the French LFS, we can see that the

transitions from the private and semi-public sectors to of these jobs jobs not reported in the DADS

are limited. Finally, another limitation of the DADS data is that we do not know the reason why

the job ended. Nevertheless, workers who quit volontarly are still eligible for benefits but after

four months of unemployment. We do not see any spike at four months in the data. Besides, a

worker who volontary quits is likely to quit his current job to another (more attractive) job. For

that reason we exclude very short unemployment spell (less than a week).

3.2 The sample

The analysis sample includes male between 30 and 50 having a non employment spells starting

between July 2001 and December 20029. For most of the workers, the eligibility depends on the

number of days worked in the past 18 months (see Table 7 in Appendix). All workers in our sample

satisfy the eligibility criteria. We exclude workers who were employed in sector with different

eligibility rules10. We may thus exclude some workers who are eligible, but we are reasonably

sure about the eligibility of the workers in our sample. For all spells, we build a 24 months

observation window, the spell being censored after 24 months. As mentionned before, we only

consider unemployment spell above 7 days. Table 8 in Appendix describes the composition of the

sample.

8Errors in the identification of individuals concern about 5% of the original sample.9Between July 2001 and December 2002 the design of the unemployment insurance system has remained un-

changed.10Especially, we drop workers from the so-called semi-private sector (this accounts for 6,3% of the outflows from

employment in 2001 and 2002). See the details of our sample selection in Appendix.

10

Table 2 shows the take-up rates in our sample, unconditional and conditional on the time spent

out of unemployment. The observed take-up rates are around 30%, a result comparable to the one

obtained by Anderson and Meyer [1997] on their sample of outflows from employment. Observed

take-up rates clearly increase with the time spent out of unemployment.

Table 2: Take-up rates unconditional and conditional on duration out of employment

All Unskilled Skilled

Unconditional % 31.65 31.26 32.33N 5712 3600 2112

Total unemployment duration>4 weeks % 35.6 34.79 37.07

N 5672 3570 2102>12 weeks % 43.15 42.56 44.19

N 5324 3366 1958> 26 weeks % 47.71 47.56 47.97

N 4734 3006 1728> 39 weeks % 48.72 48.56 49

N 4288 2715 1573> 52 weeks % 50.37 50.5 50.15

N 3971 2505 1466

This runs along with the differences in unemployment duration between those who take up and

those who do not displayed in Figure 2 . hence, the duration to registration is likely to be non

randomly right-censored. Before going to the estimation of our structural model, we estimate a

competing risks model with unobserved heterogeneity to account for the endogenous censoring and

to serve as guidelines for our empirical specification. Such a model is implicitely very similar to

the model presented above. Its results are likely to be more informative about the main features

of the data than the logit regression presented in Section 2. The details of the model are presented

in Appendix and results are displayed in Table 3.

Endogenous censoring affects only marginally the link between the reference wage and the exit

rate to registration. Higher reference wages positively affect both the exit rate to registration and

the exit rate from employment. Covered work experience no longer significant has a positive effect

on the return to employment but, perhaps surprisingly, negative on the receipt of unemployment

insurance. Individuals with stable employment trajectory are likely to find a job quickly. In that

case, their claiming effort is lower although they are entitled to longer unemployment benefits

duration. The coefficients of the distribution of unobserved heterogeneity imply that there exists a

negative correlation between the log of risk-specific unobserved components. Individuals who are

11

Employment risk Compensation riskhigh skilled -0,13 *** -0,05 ***

0,019 0,023log(reference wage) 0,11 *** 0,09 ***

0,017 0,020previous covered experience (ref: 4 to 6 months)6 to 12 months 0,51 *** -0,80 ***

0,044 0,029more than 12 months 0,69 *** -1,26 ***

0,038 0,022baseline hazard (weeks)0-2 -4,67 *** -1,79 ***

1,429 0,1422-4 -4,33 *** -3,29 ***

1,429 0,1454-8 -4,39 *** -3,75 ***

1,430 0,1448-16 -4,77 *** -4,23 ***

1,431 0,14416-30 -5,31 *** -4,91 ***

1,432 0,14630-52 -5,54 *** -5,16 ***

1,432 0,147>52 -6,74 *** -5,89 ***

1,434 0,147unobserved heterogeneitynu 1 0,00 0,00nu 2 -0,08 0,00

1,453 0,081probabilitiesPbb 0,00Pbh 0,01Phb 0,53Phh 0,46

Table 3: Competing risks model

12

Table 4: Moments on the analysis sample

Censoring in N 7.0%

Share of workers making N → P 26.0%

Share of workers making N → J 66.8%

Share of workers making N → J (within 3 months) 55.7%

Average duration in N given N → P 2.0 months

Average duration in N 4.7 months

more likely to register are less likely to find a job quickly11. Our model is especially designed to

account for such a selection process.

For the preliminary results reported here, data are transformed to monthly data and we select

only skilled workers (> high school). We end up with 7481 observations. Moments on the analysis

sample are reported in Table 4. These moments will be used latter to check our ability to replicate

the main features of the data.

On this estimation sample, the take-up rate is 26.0% and two-third of the sample makes a direct

transition between uninsured unemployment (state N) and employment, most of them within three

months. For those we receive the UI, the average duration without insurance is about 2 months

which is a sign of significant claiming frictions. The estimation of our structural model will provide

estimations of these frictions.

3.3 Empirical specification.

In order to estimate our model, we need to specify functionnal forms for the utility functions, job

offer distribution and arrival rates. Remember that, for each possible combination of observed and

unobserved variables, we need to solve our model to find the optimal search efforts, the claiming

effort and the reservation wages. These values are needed to compute the contribution of the

individuals to the likelihood. Generally speaking, the empirical specification must balance between

a framework that must be rich enough and computational limits12.

For an individual i, the utility function reads uij(wi) = log(aj + bj lnwi), with w the monthly

wage corresponding to the last employment spell. The discount rate ρ is set to .005. We solve the

model on a discrete wage grid (100 points). When a wage does not equal any point on the grid,

11Given our specification, the covariance between log(νR) and log(νJ) isaJσ

2w1

+bJσ2w2√

(a2Jσ2w1

+b2Jσ2w2

)(σ2w1

+σ2w2

)(Kamionka et

al. [2001]).12The estimations are programmed in Fortran 90 but run on a desktop computer located in the DARES (ministry

of social affairs). This computer has not been especially chosen for intensive computional tasks.

13

we use interpolation to obtain worker’s optimal efforts. Data may exhibit a positive correlation

between the exit rate from unemployment and the past wage. Unobserved heterogeneity is also

essential to understand the selection into the UI. To be able to mimic these aspects, we assume

that the arrival rates are:

λiN = exp(m0N +m1N lnwi + νi)

γi = exp(m0γ +m1γ lnwi + cγνi)

λiP = exp(m0P +m1P lnwi + cP νi)

where νi, an unobserved random effect, is normally distributed N(0, σν). In this version of the

estimation, we fix the m1s parameters to zero. We assume that job offers are drawn in a shifted

log-normal

FOffers(w) = FNormal

(lnw − lnwinf − µF

σF

)The lower bound winf is set to 300 euro . Finally, we need to characterize the value of employment

J for a worker coming from unemployment and paid at a wage wnew.

ρJ(wnew) = wnew + q (E[value of unemployment]− J(wnew)) + λJ

∫w

(J(x)− J(wnew)) dF (x)

where q stands for the job destruction rate, λJ for the job-to-job arrival rate which is assumed

exogenous. Depending on the assumptions on J , the model can be relatively straightforward or

very complicated to solve. In this version of the paper, we add the following assumptions:

• there is no job-to-job mobility (λJ = 0) (this is not a crucial assumption, it will be relaxed

in a future version);

• the job destruction rate is set to q = .003 to match the average employment duration in the

data;

• the expectation in state J about the value of employment corresponds to what the worker just

experienced (VN or VP depending on where the worker comes from). This is a key assumption

because it simplifies the expression for the reservation wage and thus speeds up dramatically

the computations.

• there is no limit to the duration of the unemployment compensation (µ = 0) and thus we

14

discard state L. We do not record transitions from state P to state L and assume the worker

stays in P (this is not a crucial assumption, it is made to get benchmark estimation and will

be relaxed thereafter in a future version).

3.4 Maximum likelihood estimation

We follow individuals from their transition from employment into non-registered unemployment

until their transition to employment if any. For each worker, we observe his unemployment history

that is his transitions between the unemployment states and the durations Dij in months in each

state. If the worker finds a job, we also observes his reemployment wage.

As an example, consider an eligible worker i. Assume that he begins in state N , moves to P

after DiN periods and finds a job with a wage wri after DiP periods in this state. His contribution

to the likelihood amounts to:

`i(DiN , DiP , DiL = 0, wi|θ, wpi , ti, Xio) = exp(−(λiNe∗iN F (R∗iN ) + γiδ

∗i )DiN )× γiδ∗i

× exp(−(λiP e∗iP F (R∗iP ) + µi)DiP ))× λiP e∗iP × f(wi)

Then this contribution must be integrated with respect to the unobserved heterogeneity parameter

ν which affects the λs and γ. The other contributions are similar and easily derived from the

model (see in Appendix). Recall that the optimal values depend on the structural parameters and

the worker’s characteristics. Identification of these parameters rely on the observed duration and

reemployment wages. One of the usual difficulty of this type of models comes from the fact that,

for some individuals, we may predict reservation wages above the observed reemployment wages.

To deal with this problem, we assume that log-wages are observed with an error which is i.i.d across

job spells and individuals and is distributed according to a log-normal distribution with mean 1

and variance σε. To reduce the set of parameters to estimate in this preliminary attempt, σε is set

to one but will be estimated in the next version of the paper.

4 Results

Before commenting the parameters’ value (reported in Table 6), it is useful to check the ability

of our model given these estimates to fit the basic features of the data. For that purpose, we

run simulations with the same observation window (18 months) and workers’ characteristics (same

distribution of past wage). Results are displayed in Table 5. The unemployment-to-job transition

moments are reasonably well fitted: both the share of workers and the duration are matched.

15

Real data Sim. data 13

Share of workers making N → J 66.8% 61.7%

Share of workers making N → J (within 3 months) 55.7% 54.2%

Average duration in N given N → P 2.0 2.5

Average duration in N 4.7 3.9

Censoring in N 7.0% 1.7%

Share of workers making N → P 26.0% 36.5%

Table 5: Comparison of the moments on the analysis sample and the same moments on simulateddata

However, our model do not generate enough censoring in state N . The main reason is obvious if

one looks at the last moments (share of workers switching from state N to state P ). The model

tends to over-estimate the take-up rate. The claiming frictions are thus underestimated. We will

return to that point later and now consider the estimated parameters’ value.

Results are reported in Table 6. We first look at the parameters relating the instantaneous

utility in unemployment and the worker’s past wage. The constants are almost null and that the

“replacement rates” are ranked as expected (bN < bP ). Notice that bP is low when compared with

the actual UI rules. Indeed, the replacement rates are supposed to be around 60% on the paper.

However, the wage used to determine the unemployment benefits is not the exact previous wage

since it excludes some form of compensation. The “real” replacement rate can thus be lower that

the official replacement rate (which is a well known fact). Moreover, the value in term of utility of

the unemployment compensation might be lower than its monetary value.

The instantaneous utility is higher in state P (because of the receipt of UI). This does mean that

the intertemporal utility is necessary higher since the different unemployment states correspond to

different job search technology. We can first compare the relative efficiency of the search technologies

by looking at λN and λP for the median individual (νi = 0): λN = 2.80 and λP = 0.66. There is a

clear loss in term of job search efficiency between state N , where the worker does not receive any

compensation, and state P , where he is registered at the unemployment insurance. This, together

with higher unemployment income, divide the exit rate from unemployment by more than two both

because the worker decreases his search intensity and increases his reservation wage (see Figure 2

which displays the exit rate from unemployment in both state).

Given that the cost functions are identical, they can also directly compared γ, the index of the

claiming frictions, with the λs. For the median worker, νi = 0, γ = 1.39. The claiming frictions

are thus substantial. If the worker spends on units of search effort and one unit of claming effort

16

Est. s.d.

aN 1.35 (.0050)

aP 0.00 (.0001)

bN 0.17 (.0091)

bP 0.27 (.0072)

µF 6.16 (.0049)

σF 0.43 (.0007)

σν 7.20 (.0019)

cP −0.62 (.0002)

cγ 0.44 (.0000)

mN 1.03 (.0002)

mP −0.41 (.0000)

mγ 0.33 (.0001)

Table 6: Parameters’ estimates

(for the same cost in term of utility since the cost functions are identical), his job arrival rate in

state N amounts to 2.80 while he switches to state P at a rate 1.39. The claiming frictions are

thus twice higher.

As mentionned before, we over-predict the take-up rate and thus probably underestimate the

claiming frictions. Which feature of the model may drive this problem. Figure 2 displays the

estimated exit rates (eNλN F (RN ), ePλP F (RP ) and γδ) as a function of the past wage. The

level of one curve with respect to the others reflects our estimations of the job arrival rates and

claiming friction parameter. Notice that the unemployment-to-job exit rate is a decreasing function

of the past wage. This comes from the positive relationship between the instantaneous utilities

(and thus values of unemployment) and this wage. Unfortunately, the negative correlation of

the unemployment exit rate and past wage is not confirmed on real data. The estimation of a

competitive risk model (see above) shows the opposite correlation. High wage workers are also

more efficient in job search or unemployment insurance claiming. Our model could reproduce

the right correlation if we allow the λs and γ to depend on w. The estimation presented here

assume m1j = 0. We thus need to relax this hypothesis. Nonetheless, in comparison with the

estimated search frictions, our estimation of the claiming frictions are already striking and show

how significant they can be.

17

0  

0.05  

0.1  

0.15  

0.2  

0.25  

0.3  

0.35  

0.4  

0.45  

0   1000   2000   3000   4000   5000   6000   7000  

N-­‐>P  transi,on  rate  

0  

0.05  

0.1  

0.15  

0.2  

0.25  

0.3  

0.35  

0.4  

0.45  

0   1000   2000   3000   4000   5000   6000   7000  

P-­‐>J  transi,on  rate  0  

0.05  

0.1  

0.15  

0.2  

0.25  

0.3  

0.35  

0.4  

0.45  

0   1000   2000   3000   4000   5000   6000   7000  

N-­‐>J  transi,on  rate  

Figure 2: Exit rate profiles as a function of past wages (simulated data)

5 Conclusion

This paper provides a model that incorporates take-up of the unemployment insurance in a job

search framework. The worker faces claiming frictions and the receipt of UI takes time and effort.

The model provides a simple way to model selection into participation and sheds new light on the

link between the job search and the claiming efforts. It is estimated using a unique administrative

database providing detailed informations about the worker’s labor market history and claiming

behaviors. We show that claiming frictions are substantial and higher than job search frictions.

In this version of the paper, some assumptions have been made that needed to be relaxed.

Especially, the arrival rates should be a function of the past wage and we need to account for the

heterogeneity in the entitled UI durations. The aim of this paper is also to provide conterfactual

experiments to assess precisely the welfare cost of the claiming frictions: this can be done be

comparing the welfare levels given our estimates and a situation where there isn’t such frictions,

that is where the workers switch immediately between N and P (γ →∞).

18

6 Appendix

The eligbility rules. Table 7 displays the UI duration as a function fo the number of months

worked in the past months.

Covered work Age Maximal length

experience of compensation

4 months in the past 18 months - 4 months

6 months in the past 12 months - 7 months

8 months in the past 12 months < 50 years old 15 months

≥ 50 years old 21 months

14 months in the past 24 months < 50 years old 30 months

≥ 50 years old 45 months

27 months in the past 36 months between 50 and 54 years old 45 months

≥ 54 years old 60 months

Source: Unedic

Table 7: Potential benefit duration (January 2001 - December 2002)

19

Table 8: Sample Composition

All Skilled Unskilled

N 18048 6533 11515Share of skilled workers 36.20Occupation in previous job

artisans and sellers 2.12 5.86white collar 14.95 41.30intermediary 19.13 52.84employees 10.83 16.98workers 52.97 83.02

Age in 200131 14.75 14.57 14.8533 13.62 13.35 13.7835 12.52 12.60 12.4837 12.44 11.83 12.7839 10.78 10.49 10.9541 8.87 9.46 8.5443 7.76 8.11 7.5645 6.17 6.72 5.8647 6.83 6.77 6.8649 6.26 6.11 6.34

Maximal compensation duration4 months 4.73 2.10 6.237 months 3.28 1.47 4.3115 months 6.29 3.63 7.8030 months 85.70 92.81 81.67

A competing risks model. We estimate a competing risks model with unobserved heterogene-

ity. Formally, let TJ and TR be two competing latent duration processes representing the durations

spent in unregistered non employment until reemployment and the completion of the claiming pro-

cess, respectively. Given the risk-specific observed and unobserved characteristics, TJ and TR are

assumed independent: TJ | XJ , νJ⊥TR | XR, νR.

Let C be the censoring process. We observe min{TJ , TR, C}. TR is censored in two circum-

stances: if the worker exits to employment before his potential claim succeeds, or is still unemployed

and unregistered one year after job separation14. In a mixed proportional hazard framework (Lan-

caster [1999], van den Berg [2001]), the likelihood function writes:

14This second type of censoring derives from entitlement rule which require that the individual must claim withina year).

20

L(tJ , tR | XJ , XR; Θ) =N∏i=1

∫ +∞

−∞`(tJ , tR | XJ , XR; Θ)g(ν)dν

where `(tJ , tR | XJ , XR; Θ) is the individual contribution to the likelihood,

`(tJ , tR | XJ , XR; Θ) =(h

(0)J (tJ) exp(XJβJ + νJ)

)δJ(h

(0)R (tR) exp(XRβR + νR)

)δR× exp

(−∑k=J,R

exp(Xkβk + νk)

∫ t

0h

(0)k (s)ds

)with Θ the set of parameters to be estimated, (Xk,νk) the observed and unobserved attributes,

h(0)k (.) the k-specific baseline hazard (k = J,R), δk risk-specific censoring dummy and g(.) the joint

distribution of the νks. The results reported in Table ?? derives from the estimations of models

parametrically specified, with Weibull-type baseline hazards. We retain a discrete distribution for

the unobserved heterogeneity. We take a two factor loading specification: νk = exp(akw1 + bkw2)

with w1 and w2 two independent discrete random variables such that w1 ∈ {0, wb1} and w2 ∈ {0, wb2}.For identification, we set aR = bR = 1. The parameters to be estimated then are aJ , bJ , wb1, wb2and the probabilities of the distribution, Pm with m = 1, ..., 4.

21

References

Adda J. and Cooper R. [2002], Dynamic Economics, The MIT Press.

Aizer A. and Currie J. [2004], “Networks or Neighborhoods? Correlations in the Use of Publicly-

Funded Maternity Care in California”, Journal of Public Economics, 88(12), 2573-2585.

Anderson P. M. and Meyer B. D. [1997], “Unemployment Insurance Take-up Rate and the

After-Tax Value of Benefits”, Quarterly Journal of Economics, 112(3), 913-937.

Black D., Smith J., Berger M. and Noel B. [2003], “Is the Threat of Reemployment Ser-

vices More Effective than the Services Themselves? Evidence from Random Assignment in the UI

System”, American Economic Review 93(4): 1313-1327.

Van den Berg G.J. [2001], “Duration models : specification, identification and multiple dura-

tions”, in Heckman J. and E .Leamer (eds.), Handbook of Econometrics Vol.5.

Van den Berg G.J. and Eckstein Z. [2003], “Empirical Labor Search: a survey”, IZA Working

Paper n◦929.

Van den Berg G.J. and van der Klaauw B. [2006], “Counseling and Monitoring of Unemployed

Workers: Theory and Evidence from a Controlled Social Experiment”, International Economic

Review, 47, 895-936.

Bertrand M., Luttmer E. and Mullainathan S. [2000], “Network Effects and Welfare Cul-

tures”, Quarterly Journal of Economics, 115(3), pp. 1019-1055.

Blank R. M. and Card D. E. [1991], “Recent Trends in Insured and Uninsured Unemployment:

Is There an Explanation”, Quarterly Journal of Economics, 106(4), 1157-1189.

Clark A.E. [2003], “Unemployment as a social norm: psychological evidence from panel data”,

Journal of Labor Economics, 21(2), 289-322.

Currie J. [2006], “The Take-up of Social Benefits”, forthcoming in Auerbach A., Card D. and J.

Quigley (eds.), Poverty, the Distribution of Income, and Public Policy, (New York: Russell Sage).

Duclos J.-Y. [1995], “Modeling the Take-Up of State Support”, Journal of Public Economics, 58,

391-415.

Gorter C. and Kalb G.R.J. [1996], “Estimating the Effect of Counseling and Monitoring the

Unemployed Using a Job Search Model” The Journal of Human Resources, Vol. 31, No. 3, pp.

590-610.

Heckman J. and Smith J. [2004], “The Determinants of Participation in a Social Program:

Evidence from a Prototypical Job Training Program”, Journal of Labor Economics 22(4): 243-298.

22

Hernandez M. and Pudney S. [2007], “Measurement error in models of welfare participation”,

Journal of Public Economics, 91(1-2), 327-341.

Hernanz V., Malherbet F. and Pellizari M. [2004], “Take-up of Welfare Benefits in OCDE

Countries: A Review of the Evidence”, OCDE.

Hopenhayn H. and Nicolini J. P. [1997], “Optimal Unemployment Insurance”, Journal of

Political Economy, 105 (2), 412-438.

Lancaster T. [1990], The econometric analysis of transition data, Cambridge University Press.

McCall B. [1995], “The Impact of Unemployment Insurance Benefit Levels on Recipiency”, Jour-

nal of Business and Economics Statistics, 13(2).

McVicar D. [2008], “Job search monitoring intensity, unemployment exit and job entry: Quasi-

experimental evidence from the UK”, Labour Economics, Vol. 15, No. 6, pp. 1451-1468.

Moffit R. [1983], “An Economic Model of Welfare Stigma”, American Economic Review, 73(3),

1023-1035.

Shavell S. and Weiss L. [1979], “Optimal Payment of Unemployment-Insurance Benefits over

Time”, Journal of Political Economy, 87 (6), 1347-1362.

Shimer R. and Werning I. [2006], “On the Optimal Timing of Benefits with Heterogeneous

Workers and Human Capital Depreciation”, Working Paper.

Storer P. and Van Audenrode M. A. [1995], “Unemployment insurance take-up rates in

Canada, determinants and implication”, Canadian Journal of Economics, 28(4), 822-835.

23